Estimating entropy production by machine learning of short-time fluctuating currents

Area of Science:

• * Statistical mechanics
• * Non-equilibrium thermodynamics
• * Machine learning

Background:

• * Thermodynamic uncertainty relations (TURs) provide lower bounds on entropy production using current mean and variance.
• * TURs are promising for estimating entropy production from limited trajectory data due to their independence from full dynamics.
• * Estimating entropy production is crucial for understanding non-equilibrium systems.

Purpose of the Study:

• * To develop a theoretical framework for estimating entropy production rates using TURs and machine learning.
• * To investigate the exact estimation of entropy production without prior knowledge of stochastic dynamics parameters.
• * To generalize TURs for subsystems and explore their hierarchical structure in estimation.

Main Methods:

• * Derivation of a short-time TUR applicable to Langevin dynamics.
• * Development of machine learning-based estimators (e.g., gradient ascent) utilizing the short-time TUR.
• * Numerical experiments on nonlinear Langevin dynamics.
• * Analysis of Markov jump processes for comparison.

Main Results:

• * A short-time TUR was derived, providing the exact entropy production rate for Langevin dynamics under optimal current selection.
• * The framework successfully estimates entropy production in nonlinear Langevin dynamics via machine learning.
• * Generalization of TURs for partial entropy production in subsystems was established.
• * Exact estimation was found to be generally impossible for Markov jump processes.

Conclusions:

• * A novel machine learning-based platform enables exact entropy production rate estimation from limited data using TURs.
• * This approach offers a powerful tool for analyzing non-equilibrium stochastic dynamics, including biological systems.
• * The study advances the application of TURs beyond lower bounds, offering precise estimations.